Euclidean Geometry

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Euclid's Elements

A. C. McKay,R. A. Thompson
Euclid s Elements Book PDF

Author : A. C. McKay,R. A. Thompson
Publisher : Wentworth Press
Page : 252 pages
File Size : 43,9 Mb
Release : 2016-08-26
Category : History
ISBN : 1362401757

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Euclid's Elements by A. C. McKay,R. A. Thompson Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Advanced Euclidean Geometry

Roger A. Johnson
Advanced Euclidean Geometry Book PDF

Author : Roger A. Johnson
Publisher : Courier Corporation
Page : 338 pages
File Size : 55,7 Mb
Release : 2013-01-08
Category : Mathematics
ISBN : 9780486154985

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Advanced Euclidean Geometry by Roger A. Johnson Pdf

This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.

Euclid's Elements (the Thirteen Books)

Euclid
Euclid s Elements the Thirteen Books Book PDF

Author : Euclid
Publisher : Unknown
Page : 404 pages
File Size : 53,7 Mb
Release : 2017-12-17
Category : Mathematics
ISBN : 1420956477

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Euclid's Elements (the Thirteen Books) by Euclid Pdf

Euclid was a mathematician from the Greek city of Alexandria who lived during the 4th and 3rd century B.C. and is often referred to as the "father of geometry." Within his foundational treatise "Elements," Euclid presents the results of earlier mathematicians and includes many of his own theories in a systematic, concise book that utilized a brief set of axioms and meticulous proofs to solidify his deductions. In addition to its easily referenced geometry, "Elements" also includes number theory and other mathematical considerations. For centuries, this work was a primary textbook of mathematics, containing the only framework for geometry known by mathematicians until the development of "non-Euclidian" geometry in the late 19th century. The extent to which Euclid's "Elements" is of his own original authorship or borrowed from previous scholars is unknown, however despite this fact it was his collation of these basic mathematical principles for which most of the world would come to the study of geometry. Today, Euclid's "Elements" is acknowledged as one of the most influential mathematical texts in history. This volume includes all thirteen books of Euclid's "Elements," is printed on premium acid-free paper, and follows the translation of Thomas Heath.

Euclidean Geometry in Mathematical Olympiads

Evan Chen
Euclidean Geometry in Mathematical Olympiads Book PDF

Author : Evan Chen
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 50,9 Mb
Release : 2021-08-23
Category : Education
ISBN : 9781470466206

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Euclidean Geometry in Mathematical Olympiads by Evan Chen Pdf

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.

Euclidean Geometry

Mark Solomonovich
Euclidean Geometry Book PDF

Author : Mark Solomonovich
Publisher : iUniverse
Page : 411 pages
File Size : 40,8 Mb
Release : 2010
Category : Education
ISBN : 9781440153488

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Euclidean Geometry by Mark Solomonovich Pdf

This textbook is a self-contained presentation of Euclidean Geometry, a subject that has been a core part of school curriculum for centuries. The discussion is rigorous, axiom-based, written in a traditional manner, true to the Euclidean spirit. Transformations in the Euclidean plane are included as part of the axiomatics and as a tool for solving construction problems. The textbook can be used for teaching a high school or an introductory level college course. It can be especially recommended for schools with enriched mathematical programs and for homeschoolers looking for a rigorous traditional discussion of geometry. The text is supplied with over 1200 questions and problems, ranging from simple to challenging. The solutions sections of the book contain about 200 answers and hints to solutions and over 100 detailed solutions involving proofs and constructions. More solutions and some supplements for teachers are available in the Instructor's Manual, which is issued as a separate book. Book Reviews: 'In terms of presentation, this text is more rigorous than any existing high school textbook that I know of. It is based on a system of axioms that describe incidence, postulate a notion of congruence of line segments, and assume the existence of enough rigid motions ("free mobility")... My gut reaction to the book is, wouldn't it be wonderful if American high school students could be exposed to this serious mathematical treatment of elementary geometry, instead of all the junk that is presented to them in existing textbooks. This book makes no concession to the TV-generation of students who want (or is it the publishers who want it for them?) pretty pictures, side bars, puzzles, games, historical references, cartoons, and all those colored images that clutter the pages of a typical modern textbook, while the mathematical content is diluted more and more with each successive edition.' Professor Robin Hartshorne, University of California at Berkeley. 'The textbook "Euclidean Geometry" by Mark Solomonovich fills a big gap in the plethora of mathematical textbooks - it provides an exposition of classical geometry with emphasis on logic and rigorous proofs... I would be delighted to see this textbook used in Canadian schools in the framework of an improved geometry curriculum. Until this day comes, I highly recommend "Euclidean Geometry" by Mark Solomonovich to be used in Mathematics Enrichment Programs across Canada and the USA.' Professor Yuly Billig, Carlton University.

Euclidean Geometry

David M. Clark
Euclidean Geometry Book PDF

Author : David M. Clark
Publisher : American Mathematical Soc.
Page : 157 pages
File Size : 46,7 Mb
Release : 2012-06-26
Category : Mathematics
ISBN : 9780821889855

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Euclidean Geometry by David M. Clark Pdf

Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation. Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry. The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority. This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Geometry: Euclid and Beyond

Robin Hartshorne
Geometry Euclid and Beyond Book PDF

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 44,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9780387226767

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Geometry: Euclid and Beyond by Robin Hartshorne Pdf

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.

Euclidean Geometry and Transformations

Clayton W. Dodge
Euclidean Geometry and Transformations Book PDF

Author : Clayton W. Dodge
Publisher : Courier Corporation
Page : 306 pages
File Size : 45,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138428

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Euclidean Geometry and Transformations by Clayton W. Dodge Pdf

This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.

Low-Dimensional Geometry

Francis Bonahon
Low Dimensional Geometry Book PDF

Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 44,9 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9780821848166

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Low-Dimensional Geometry by Francis Bonahon Pdf

The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

Problems and Solutions in Euclidean Geometry

M. N. Aref,William Wernick
Problems and Solutions in Euclidean Geometry Book PDF

Author : M. N. Aref,William Wernick
Publisher : Courier Corporation
Page : 274 pages
File Size : 41,8 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486477206

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Problems and Solutions in Euclidean Geometry by M. N. Aref,William Wernick Pdf

Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.

Introductory Non-Euclidean Geometry

Henry Parker Manning
Introductory Non Euclidean Geometry Book PDF

Author : Henry Parker Manning
Publisher : Courier Corporation
Page : 110 pages
File Size : 48,6 Mb
Release : 2005-02-18
Category : Mathematics
ISBN : 9780486442624

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Introductory Non-Euclidean Geometry by Henry Parker Manning Pdf

This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. Major topics include hyperbolic geometry, single elliptic geometry, and analytic non-Euclidean geometry. 1901 edition.

Elementary Euclidean Geometry

C. G. Gibson
Elementary Euclidean Geometry Book PDF

Author : C. G. Gibson
Publisher : Cambridge University Press
Page : 194 pages
File Size : 48,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0521834481

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Elementary Euclidean Geometry by C. G. Gibson Pdf

This book, first published in 2004, is an example based and self contained introduction to Euclidean geometry with numerous examples and exercises.

Methods for Euclidean Geometry

Owen Byer,Felix Lazebnik,Deirdre L. Smeltzer
Methods for Euclidean Geometry Book PDF

Author : Owen Byer,Felix Lazebnik,Deirdre L. Smeltzer
Publisher : American Mathematical Soc.
Page : 461 pages
File Size : 53,8 Mb
Release : 2010-12-31
Category : Mathematics
ISBN : 9780883857632

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Methods for Euclidean Geometry by Owen Byer,Felix Lazebnik,Deirdre L. Smeltzer Pdf

Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.

Euclidean and Non-Euclidean Geometry International Student Edition

Patrick J. Ryan
Euclidean and Non Euclidean Geometry International Student Edition Book PDF

Author : Patrick J. Ryan
Publisher : Cambridge University Press
Page : 237 pages
File Size : 42,8 Mb
Release : 2009-09-04
Category : Mathematics
ISBN : 9780521127073

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Euclidean and Non-Euclidean Geometry International Student Edition by Patrick J. Ryan Pdf

This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.

The Wonder Book of Geometry

David Acheson
The Wonder Book of Geometry Book PDF

Author : David Acheson
Publisher : Oxford University Press
Page : 240 pages
File Size : 51,7 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9780192585370

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The Wonder Book of Geometry by David Acheson Pdf

How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.